Wicked (the musical) actually holds fairly well with WoO, the book - in which the the Wicked Witch never lit the Scarecrow on fire at the end.
If you want to look at the inconsistencies, fine:
for now we shall call the Wicked Witch Elphaba - so we can compare it to Wicked.
1) Elphaba wanted to get the shoes back. Let's assume Fiyero knew this. He would want to get in good with Dorothy to steal the shoes, no?
2) Elphaba but a "spell" on Fiyero to save his life. Nothing, therefore, could kill him (fire included; remember the flying monkeys pulled out his stuffing, "well, that's you all over.")
3) Why
did Elphaba only pick on "the Scarecrow?" (like when she throws the fire at the Scarecrow.)
4) After Glinda leaves Dorothy, they sing Follow the Yellow Brick Road. In the movie, there was no corn field near the actual scene of the crime (aka Dorothy's house). Therefire, Glinda may have floated off to the corn field - with the house in the distance (remember this is OZ).
5) Elphaba went away in a blast of fire - maybe to her castle. Remember her crystal ball? Maybe she saw Glinda crying on that and decided - time to teach that blonde _________ a lesson!
6) In comes Fiyero ---
7) Meanwhile, Boq has been the tinman. He was on his way from Munchkinland to the Emerald City - following the Yellow Brick Road - when Mme. Morrible conjured up the tornado, rusting him on the side of the road.

Boq comes to and does not recognize Dorothy. or Toto - is it a plot of Elphaba? Let me pretend to have been here for a while (just as Fiyero did).
9) Between the time Elphaba turns Fiyero into the scarecrow (No Good Deed) and the March of the Witch Hunters, perhaps some time has passed. Sometime on the journey, Boq and the Lion sneaked off from Dorothy and Fiyero - to go to the "March."
10) Dorothy gets kidnapped and Boq, Fiyero, and the Lion are outside the castly waiting to find a way in. This is when Glinda comes in (For Good).
11) Elphaba goes off and gets herself "melted."